Snow storm effect without lighting
You still need to see the snow in order to tell that it is snow. Otherwise you could simply follow the tutorial and then turn off the lights. Boom! Now that's what snow looks like at night (all black). If your aim is to make a cinematic nighttime snow storm then you want to follow the same idea from a particle and physics perspective and instead tweak your lighting.

When we light rain or snow in night time, we use backlighting. This means that the source of light should be coming from the opposite side of the subject, relative to the camera. This creates an outline or 'edge' effect on the subject while leaving the front of it dark. This allows you to see the snow itself but maintain the impression of night time. Making the light a deep blue also helps simulate 'moon light'.